document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=942430>Question 942430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A fair coin is flipped 10 times. Find the probability of the occurrence of 5 or 6 heads. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #574525 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=574525\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "A fair coin<BR>\n" );
document.write( "Flipped 10 times<BR>\n" );
document.write( "  <BR>\n" );
document.write( "This means that<BR>\n" );
document.write( "1. probability of heads (success) is constant at p=0.5<BR>\n" );
document.write( "2. \"flipping 10 times\" imply random and independent outcomes over the experiment<BR>\n" );
document.write( "3. The number of trials (flip) is known.<BR>\n" );
document.write( "4. Each trial is a Bernoulli experiment (one of two possible outcomes).<BR>\n" );
document.write( "Under these conditions, the binomial distribution applies.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "The probability of r successes in n trials is given by:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X=r%29+=+C%28n%2Cr%29%2A%28p%5Er%29%2A%28q%5E%28n-r%29%29 ALIGN=MIDDLE  ALT=\"P%28X=r%29+=+C%28n%2Cr%29%2A%28p%5Er%29%2A%28q%5E%28n-r%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where C(n,r) is r combinations out of n objects = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%21%2F%28%28n-r%29%21r%21%29 ALIGN=MIDDLE  ALT=\"n%21%2F%28%28n-r%29%21r%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and q=(1-p)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Substituting values n=10, p=0.5, r=5 or 6, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X=5%29+=+C%2810%2C5%29%2A%280.5%5E5%29%2A%28%281-0.5%29%5E%2810-5%29%29=0.246 ALIGN=MIDDLE  ALT=\"P%28X=5%29+=+C%2810%2C5%29%2A%280.5%5E5%29%2A%28%281-0.5%29%5E%2810-5%29%29=0.246\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X=6%29+=+C%2810%2C6%29%2A%280.5%5E6%29%2A%28%281-0.5%29%5E%2810-6%29%29=0.205 ALIGN=MIDDLE  ALT=\"P%28X=6%29+=+C%2810%2C6%29%2A%280.5%5E6%29%2A%28%281-0.5%29%5E%2810-6%29%29=0.205\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "Probability of 5 or 6 heads is the sum of P(X=5) and P(X=6) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28X=5+or+X=6%29=0.246%2B0.205=0.451 ALIGN=MIDDLE  ALT=\"P%28X=5+or+X=6%29=0.246%2B0.205=0.451\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );